# A particle in Electric and Magnetic field

1. Jan 27, 2016

### Abdul.119

1. The problem statement, all variables and given/known data
A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

2. Relevant equations

3. The attempt at a solution
I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?

2. Jan 27, 2016

### Suraj M

What exactly is r"?

3. Jan 27, 2016

### Abdul.119

r is just position, and by r'' I mean it is r derived twice so that it is acceleration

4. Jan 27, 2016

### Suraj M

Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?

5. Jan 27, 2016

### Abdul.119

In general it should be F = ma

6. Jan 27, 2016

### Suraj M

What would be the shape of the path of the object?

7. Jan 28, 2016

### ehild

Yes, it is correct.
You know the direction of the electric and magnetic field vectors. Write them out in vector form, and determine the components Fx, Fy, Fz of the force. Note that the force depends on the velocity, that is, (x'x, y'y, z'z) , Then you get three equations in the form mx"=Fx, my"=Fy, mz"=Fz.